Using the Distributive Property to Multiply Quickly

Welcome to a video on how to use the distributive property to multiply two digit numbers quickly. Let’s start by reviewing
the distributive property. The distributive property states when we multiply a factor
and a sum or difference, we multiply the factor by each term of the sum or difference. If we have A times the quantity B plus C, we’re going to have A
times B, plus A times C, and if we have A times
the quantity B minus C, we will have A times B, minus A times C. We can use this property to help us multiply two digit numbers rather quickly, without the use of a calculator. So, let’s see if we can use
the distributive property to find this product, 52 times 11. What the distributive
property allows us to do is to rewrite this as 52 times
the quantity 10 plus one, instead of 11. The reason that’s helpful is, it’s a lot easier to
multiply by 10 and buy one, rather than by 11. 52 times 10 would be 520, plus, 52 times one would be 52. The idea is, if you can envision this, and you can find these
products in your head, you could then find this sum
to find the original product. Well, 520 plus 52 would be 572. So, 52 times 11 is equal to 572. Let’s take a look at another. Here, we have 36 times 12. Again, not an easy product
to determine in your head, but we could think of this as 36 times, instead of 12, 10 plus two. Again, the reason that’s helpful is, 36 times 10 is pretty easy to
determine, that would be 360, and 36 times two is also pretty easy to determine, that would be 72. Now, we can just determine this sum. Here, it’s a little bit more involved, because we would have to carry, but this would be equal to 432. So, 36 times 12 is equal to 432. Let’s go ahead and take
a look at one more. Here, we have 13 times 48. What we could do is think of this as 13, instead of times 48, we could
write 48 as 50 minus two. Notice now, we have a difference, but the idea here is that now
we can multiply 13 and 50, and also 13 and two, and
then find the difference. Well, 13 times 50 would be
the same as 13 times five, and then add an extra zero. 13 times five would be 65,
add a zero, we would have 650. Then, 13 times two would
be 26, so we have minus 26. Again, if we were able to memorize or store these numbers
in our mind for a moment, and then subtract, we can
see that this difference is going to be 624, therefore, 13 times 48 is equal to 624. If you like this technique, I
think with a little practice, you would be able to multiply
any two digit numbers without a calculator, or without performing multiplication
in the traditional way. Thank you for watching.